Hydrogen adsorption and dissociation on Au_nY (n = 1–12) nanoclusters: a DFT investigation

Abstract

The interaction between nanomaterial systems and hydrogen has recently emerged as a compelling study model, offering valuable insights for designing materials with applications in nanotechnology, catalysis, and energy storage. Among these, transition metal-doped gold clusters exhibits intriguing stability and electronic properties, making them promising candidates for hydrogen related processes. In this study, we employ density functional theory (DFT) to investigate the interaction between H₂ molecules and small-sized gold clusters doped with yttrium. Our finding reveals that most of the bare cluster structures remain intact during the H₂ adsorption, regardless of whether the process occurs molecularly or dissociatively. A comprehensive analysis indicates that the preferred adsorption configuration is governed by multiple factors, including adsorption site (surface vs. encapsulated), relative electronegativity, and the atomic coordination number. The calculations demonstrate that dissociative adsorption of H₂ on Au₆Y and Au₁₁Y clusters is both thermodynamically and kinetically favorable. However, for Au_nY (n = 1, 4–5, 8, 10) dissociative adsorption is hindered by a significant energy barrier before reaching the final state, while for species with n = 2, 3, 7, and 9 molecular adsorption is more favorable due to intrinsic energy preferences. This study provides fundamental insights into the adsorption sites and detailed analysis of adsorption kinetics on Au_nY clusters, laying the groundwork for further theoretical an ed experimental investigations into the hydrogenation process in nanostructured materials.

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1. Introduction

Nowadays, hydrogen has been envisioned as a key energy carrier for sustainable development of the future economy, meeting essential environmental and energy requirements.^1–3 Compared to traditional fuels like gasoline (44 MJ kg⁻¹) and diesel (45.6 MJ kg⁻¹),^4,5 hydrogen offers the highest energy density per unit mass (∼120 MJ kg⁻¹) and conversion efficiency and can be produced through water-splitting reactions without CO₂ emissions. Moreover, it can be conveniently stored in various forms, including gaseous, liquid, or metal hydrides.^6–8 However, the practical implementation of hydrogen energy storage after generation and during transport faces significant challenges, primarily due to its kinetic stability under ambient conditions and the low energy density per unit volume of solid storage materials.

To address this bottleneck, various strategies have been explored.^9–12 Among them, metal hydride materials have garnered special attention as model solid-state hydrogen storage systems, offering a more compact and secure alternative. They provide the possibility of preventing critical operating conditions like high pressures and elevated temperatures, which are typical of conventional compressed gas and liquefied hydrogen storage.¹³ To enhance the practical prospect of metal hydride, a deeper understanding of the interaction between hydrogen and potential surface at the molecule level is essential. Therefore, nanoclusters consisting of a few atoms have emerged as promising candidates for providing fundamental insights into potentially reactive sites, given significant variation in physical and chemical properties with size and composition.

Among various metal nanoclusters, gold nanoclusters (Au_n) are considered particularly advantageous due to their superior stability, abundance, and cost-effectiveness, even surpassing palladium and platinum in many aspects. While gold is chemically inert in its bulk form, it exhibits remarkable catalytic activity at the nano scale. For example, gold nanoclusters have shown promising performance in catalytic processes such as water-splitting reaction¹⁴ and CO oxidation.¹⁵ Interestingly, this catalytic behavior is highly dependent on their geometric structure. Bootharaju and co-workers¹⁶ investigated the Au₁₂Ag₃₂/TiO₂, system, which features a gold icosahedral core encapsulated by a silver dodecahedral shell. Their finding revealed a substantial enhancement in solar H₂ production efficiency, approximately 6.2 and 37.8 times higher than those of Ag₄₄/TiO₂ and bare TiO₂, respectively. Furthermore, key factors influencing the reactivity and catalytic potential of gold nanoclusters include cluster size, atomic composition, and charge state.^17–19 By tailoring these parameters, such as through doping or precise control of cluster size, researchers can design tunable materials optimized for specific catalytic processes. For instance, both experimental and theoretical studies have explored O₂ activation on small-sized anionic Aun⁻ clusters.²⁰ S. Pal and D. Manzoor have compared the catalytic efficiency of Au₈, Pd₈, Au_8−n Pd_n (n = 1–7), Au₇Si,^21,22 Au₁₈ and endohedral Au₁₈M (M = Na, K, Mg, Ca, Al, Ga) cages,²³ and Al-, Hf-, and Ge-doped Au₂₀ cages.²⁴ Similarly, Zeng and co-workers²⁵ using DFT calculation studied the catalytic behavior of sub-nanometer-sized gold nanoclusters supported on TiO₂. They observed that cluster shape and size significantly influenced catalytic performance, with adsorption energies for O₂ and CO decreasing as the cluster size increased within the range of 16–35 atoms.¹⁵ Recent studies have also highlighted the emerging role of hydrogen atoms as dopants in gold nanoclusters.²⁶ Beyond their electronegativity, hydrogen atoms can induce chemisorption and activation on previously inert or closed-shell gold clusters,²⁷ modulated by cluster shape,^28,29 and charge state.³⁰ This, in turn, enhances the adsorption and activation of O₂ and CO molecules, opening new directions for designing advanced gold-based catalysts.

Research efforts have expanded beyond the studies of O₂ adsorption and CO oxidation to include investigations of metal nanoclusters and their alloys in order to deepen our understanding of the kinetics and dynamics of hydrogenation reactions. Numerous density functional theory (DFT)^31–34 studies have investigated the adsorption and dissociation of hydrogen on metal nanoclusters. The H₂ absorption process has been found to strongly depend on the physical and chemical properties, structural, size, and composition of nanoclusters, as demonstrated in 3d transition metal (Sc–Zn)-doped Cu clusters³⁵ and Au₂₄M, Au₃₆M (M = Pt and Pd).³⁶ Theoretical studies have demonstrated that the incorporation of a Pt dopant can significantly alter the electronic structure of gold nanoclusters Au_n+1 (n = 1–12), thereby enhancing their reactivity toward H₂ molecules.³⁷ Li and coworkers investigated the effect of adsorbed hydrogen atoms on the geometric and electronic structures of alkali-doped gold nanoclusters, providing insights into hydrogen-cluster interaction.³⁸ Additionally, the adsorption and dissociation behavior of TiMg_n (n = 1–12) clusters has been examined DFT, revealing key factors that govern their hydrogen activity.³⁹ Furthermore, mass spectrometry and infrared multiple photon dissociation spectroscopy combined with theoretical calculations, have provided insights into the competition between molecular and dissociative hydrogen chemisorption, which is highly dependent on the size of cationic aluminum-doped Rh clusters.^40,41 Recently, Lan et al. conducted comparative studies on the influence of 3d transition metal atoms on hydrogen adsorption and dissociation by examining size-dependent Ag_nCr (n = 2–12) clusters and composition-dependent Au₉M²⁺ (M = Sc–Ni) clusters.^42,43 Their research has revealed that Ag₃Cr, Ag₆Cr, and Au₉Ti²⁺, clusters exhibit the ability to adsorb and dissociate H₂, leading to the formation of metal hydrides even at room temperature.

Additionally, 4d transition metal atoms have shown significant potential for hydrogen storage, attributed to their enhanced stability, fully filled electron configurations across multiple energy levels, diverse oxidation states, and distinct chemical properties compared to their 3d counterparts.^44,45 Moreover, the lower electronegativity of 4d transition metals relative to 3d elements influences their interaction with hydrogen, raising several intriguing questions, such as how charge transfer occurs in clusters and the nature of interactions between dopant clusters and hydrogen molecules. To address these questions, the effects of boron and 4d transition metal (Y–Mo) on hydrogen adsorption and storage properties have been systematically investigated.^45–47 Notably, the impact of charge transfer, electronegativity, and the atomic radius of the dopant elements on the catalytic mechanism and hydrogen storage capacity of MgH₂ clusters has been clarified.^48,49 C.S. Sergio et al. have clarified the correlation between hydrogen storage capacity and the surface binding energy of 4d transition metal-doped carbon nanoflakes.⁵⁰ Recent work by J. Barabás et al., combining gas-phase reaction investigations and DFT computations, has demonstrated that the catalytic activity of gold cation clusters (Aun⁺) and yttrium-doped gold (Au_n−1Y⁺, n = 4–20) clusters can be effectively tuned by cluster size, charge state, and dopant introduction.⁵¹ While initial studies have explored the influence of 4d transition metals on cluster stability and reactivity, a systematic investigation of the hydrogen storage mechanism in noble metal clusters doped with 4d transition metals remains lacking. A deeper understanding of the kinetics and dynamics of hydrogenation reactions in precious metal species and their alloys could pave the way for new research directions in hydrogen storage materials.^52,53

Driven by the pursuit of nanocluster materials for efficient hydrogen storage, this study aims to theoretically explore the critical role of yttrium doping in H₂ adsorption and dissociation on small gold clusters. Using DFT calculations,⁵⁴ we systematically analyze the geometrical, relative stability, bonding characteristics, electronic properties, and adsorption energies of Au_nY (n = 1–12) clusters. The insights gained from this study provide a deeper understanding of the influence of 4d transition metal dopants on hydrogen adsorption and dissociation mechanisms. Furthermore, these findings offer valuable guidelines for future experimental studies, aiding the rational design of advanced nanomaterials for hydrogen storage applications.

2. Computational method

This work uses the DFT calculations implemented in the Gaussian 09 program^55,56 in combination with GaussView, to predict the geometric and electronic structures of Au_nY (n = 1–12) clusters in their ground state, along with their molecularly and dissociatively adsorbed variants Au_nY–H₂ and Au_nY–2H. To generate initial cluster structures, two complementary approaches were employed: (1) a stochastic algorithm was used to explore a broad range of feasible Au_nY (n = 1–12) configurations;⁵⁷ (2) manual structure construction, in which a Y atom systematically replaced an Au atom at all possible positions within the cluster. Subsequently, hydrogen adsorption configurations were investigated based on the lowest-energy Au_nY (n = 1–12) structures, where a single H₂ molecule or two dissociated H atoms were attached at various adsorption sites.

Computationally, predicted structures were first optimized by the TPSSTPSS functionals in combination with the cc-pVDZ-pp basis set for Au and Y atoms, and LanL2DZ for H atoms. For each cluster size, various structural and spin configurations were explored and subjected to the convergence criteria. Nevertheless, only species with relative energies less than 2.0 eV were selected for single-point energy recalculations at the same functional level but with an enhanced basis set, specifically cc-pVTZ-pp for Au and Y atoms and LanL2DZ for H atoms. This approach represents a balanced trade-off between computational accuracy and efficiency and has been shown to be reliable for 4d transition metal-doped noble metal systems.⁵⁸ To validate the accuracy and reliability of our computational methodology, we compared binding energies (BE, eV) of Au₂, AuY, AuH, and YH dimers across different functionals, including TPSSTPSS, BP86, BPW91, BLYP, and PBEPBE. Tables 1 and S1† summarize the results and benchmarks them against available experimental data, confirming that the TPSSTPSS/cc-pVTZ-pp (for Au and Y) and LanL2DZ (for H) combination yields the closest agreement with experimental values. The self-consistent field (SCF)⁵⁹ calculations were conducted with a convergence threshold of 2.0 × 10⁻⁵ Hartree per Å for gradients and 5.0 × 10⁻³ Å for displacements. The stability of the lowest-energy structures was further confirmed by calculating harmonic vibrational frequencies, ensuring they correspond to true minima on the potential energy surface. To reinforce the robustness of the ground-state optimization, multiple spin multiplicities were examined for each structure. The electronic configurations of all lowest-energy structures were analyzed using the natural bond orbital (NBO) method.⁶⁰ To explore the reaction mechanisms, transition-state (TS) geometries were identified using the quadratic synchronous transit (QST) method,^61,62 with relaxed potential energy surface (PES) scans along appropriate internal coordinates. To further verify the transition states, intrinsic reaction coordinate (IRC) calculations were performed, ensuring a continuous and valid connection between reactants and products.

Table 1 Calculated binding energies (BE, eV) for AuH and YH dimers using various functionals in combination with cc-pVTZ-pp for Au and Y atoms, and LanL2DZ/SDD for H atoms

Dimer	BP86		PW91		BLYP		PBEPBE		TPSSTPSS		Experiment^63
	LanL2DZ	SDD	LanL2DZ	SDD	LanL2DZ	SDD	LanL2DZ	SDD	LanL2DZ	SDD
AuH	3.07	3.11	3.02	3.00	2.94	2.97	2.94	2.98	3.00	3.02	3.03 ± 0.08
YH	2.90	3.12	2.74	2.82	2.88	3.02	2.79	2.85	2.94	3.23	—

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3. Optimized geometrical structures

We first optimized the lowest-energy structures of bare Au_nY clusters and then examined both molecular and dissociative adsorption of hydrogen, leading to the formation of Au_nY–H₂ and Au_nY–2H clusters, respectively. To ensure the stability of the obtained geometries, we conducted frequency calculations, confirming the absence of imaginary frequencies in all optimized structures. While multiple geometrical and spin isomers exist for each stoichiometry, only the lowest-energy structures of Au_nY, Au_nY–H₂, and Au_nY–2H clusters were selected for further discussion of hydrogen adsorption behavior, as shown in Fig. 1. Other low-lying isomers for Au_nY–H₂ and Au_nY–2H clusters are provided in the ESI.† ⁴⁶

Fig. 1 Optimized structures of Au_nY, Au_nY–H₂, and Au_nY–2H clusters (n = 1–12). The yellow, purple, and red spheres represent Au, Y, and H atoms, respectively.

Our results indicate that the stable spin configurations of Au_nY (n = 1–12) clusters follow an alternating pattern with a singlet spin state for odd n and a doublet for even n. The lowest-energy Au_nY structures tend to adopt a cage-like form as the cluster size increases, where the Y atom prefers a highly coordinated position. Interestingly, the structural framework of Au_nY (n = 1–12) clusters undergoes significant reconstruction upon yttrium doping, deviating from the planar configuration of pure Au_n clusters (n ≤ 11).⁶⁴ Unlike pure gold clusters, where the first 3D structure appears at n = 12, the introduction of a Y atom stabilizes 3D geometries at much smaller sizes, starting from n = 4, where four Au atoms coordinate around the Y dopant. The lowest-lying isomers of Au_nY (n = 5–8) retain a 2D morphology, whereas larger clusters (n = 9–12) exhibit 3D structural preferences. These findings align well with theoretical predictions and far-infrared spectral studies of yttrium-doped gold clusters.⁶⁵

Our calculations suggest that hydrogen adsorption does not significantly alter the geometric structure of bare Au_nY clusters, except for Au₅Y, where H₂ preferentially attaches to energetically unstable bridge sites (Au–Y and Au–Au). Similar behavior has been observed in transition metal-doped clusters.^41–43,66 For Au_nY (n = 1–5, 7, 9, and 12), the hydrogen molecule favors direct attachment to the Y dopant, attributed to differences in electronegativity χ between Y (1.22), H (2.2), and Au (2.54). Fundamentally, hydrogen bonding arises from electrostatic attraction, facilitated by charge transfer between atoms with significant electronegativity differences. Consequently, bonds between the low-electronegativity Y atom and high-electronegativity H atom are more favorable, in agreement with previous reports, where surface impurities are among the most favored adsorption sites for a hydrogen molecule on transition metal doped clusters.^41–43,67 Furthermore, hydrogen adsorption is not solely governed by electronegativity differences but also strongly influenced by atomic coordination number (N). Lower coordination numbers correspond to higher surface activity, facilitating stronger H₂ adsorption.⁶⁸ Consequently, atomic clusters with low-coordination sites exhibit enhanced hydrogen interaction capability. For example, experimental and theoretical studies on singly rhodium-doped cationic aluminum clusters (Al_nRh⁺) using time-of-flight mass spectrometry and infrared multiple photon dissociation, in combination with DFT calculations, have demonstrated that hydrogen preferentially binds to the Al atom rather than the Rh impurity in cluster sizes where Rh is coordination-saturated or encapsulated.⁴¹ This principle helps explain the behavior observed in Au₆Y–H₂, Au₈Y–H_2, Au₁₀Y–H₂, and Au₁₁Y–H₂ clusters, where a competition between electronegativity and coordination occurs as H₂ preferentially attaches to a low-coordination Au vertex (N_Au = 2 or 3) instead of the highly coordinated Y impurity (N_Y = 6, 8, or 9). A similar hydrogen adsorption trend has been reported for the clusters Al_nCr, Ag_nCr, Au₉M²⁺, Al_nRh²⁺, and Mg_nCo, further reinforcing the critical role of coordination number in determining the preferred hydrogen adsorption site.^{41–43,66,69}

Upon molecular adsorption, the hydrogen molecule may dissociate, triggering a structural transformation of the bare clusters.⁷⁰ However, the ground-state geometry of Au_nY clusters generally remains intact upon hydrogen adsorption, with only minor distortions observed in Au₂Y–2H, Au₅Y–2H, and Au₈Y–2H. As illustrated in Fig. 1, following H₂ dissociation one Au atom shifts closer to another Au atom in Au₂Y–2H, while in Au₅Y–2H and Au₈Y–2H, a single Au atom is slightly displaced from two-membered and three-membered Au chains, respectively. Notably, both cluster size and the position of the Y dopant significantly influence H₂ dissociation and adsorption behavior, which can be categorized into two distinct trends. For small clusters (n = 2–4), individual hydrogen atoms preferentially bind to the surface Y atom, typically at the Au–Y bridge site. As the cluster size increases (n = 5–12), the Y atom becomes progressively encapsulated by surrounding Au atoms, leading to H atoms favoring Au–Au bridge adsorption rather than direct interaction with Y. This trend is in good agreement with previous investigations.⁴³ In the case of AuY–2H, both H atoms preferentially adsorb on top of the Y surface site, highlighting the role of dopant coordination and atomic arrangement in governing hydrogen interaction dynamics.

4. Relative stability

The relative stability of a clusters is a key parameter that provides insight into its bonding or dissociation energy, which are critical in determining reactivity and stability in chemical reactions. This stability is typically assessed through average binding energies (BE, in eV) calculations. The BE is defined as the mean energy difference between the sum of the total energies of all isolated constituent atoms and the total energy of the cluster. The calculation follows the equations below:Here, E represents the total energy of the clusters or individual atoms. The binding energy (BE) values of Au_nY (n = 1–12) clusters range from 1.59 to 2.58 eV, as shown in Fig. 2 and Table 2. A notable increase in BE is observed for bare Au_nY clusters in the small-size range (n = 1–3), rising sharply from 1.59 eV to a peak of 2.55 eV. This trend persists in the presence of molecular hydrogen adsorption, although the increase in BE (from 1.96 eV to 2.48 eV) remains less pronounced compared to bare clusters of the same size. In contrast, for dissociative adsorption (Au_nY–2H), BE values gradually decrease from 2.38 eV to 2.08 eV. In contrast, the BE for dissociative adsorption Au_nY–2H exhibit a rough decrease from 2.38 to 2.08 eV. More remarkably, for larger clusters (n = 4–12), the BE values remain relatively stable, suggesting that these clusters exhibit greater stability after hydrogen release compared to smaller clusters (n = 1–3). Furthermore, the higher BE values of Au_nY–2H clusters (for n = 4–6, 8, 10 and 11) compared to their molecularly adsorbed Au_nY–H counterparts indicate that H₂ dissociation following molecular adsorption is more favorable at these sizes. This finding aligns well with the high intrinsic stability of bare Au₆Y clusters.⁶⁵ In contrast, for clusters with n = 1–3, 7, and 12, dissociative adsorption is energetically unfavorable, indicating that H₂ is more likely to remain in molecular form on these clusters.

Fig. 2 Comparison of per-atom binding energies (BE, in eV) for Au_nY, Au_nY–H₂, and Au_nY–2H cluster.

Table 2 Comparison of calculated average biding energies per atom (BE/eV), adsorption energies (E_ads/eV), and H–H bond length (d_H−H/Å) for bare Au_nY clusters, molecular (H₂), and dissociative (2H) hydrogen adsorption on Au_nY (n = 1–12)

n	BE/eV			Eads/eV		dH−H/Å
	AunY	AunY–H2	AunY–2H	AunY–H2	AunY–2H	AunY–H2	AunY–2H
1	1.59	1.96	2.38	0.12	1.81	0.81	3.36
2	2.19	2.28	2.14	0.29	−0.39	0.85	4.16
3	2.55	2.48	2.08	0.15	−2.27	0.75	2.40
4	2.43	2.40	2.42	0.16	0.27	0.76	3.35
5	2.51	2.45	2.51	0.05	0.52	0.83	3.44
6	2.50	2.46	2.51	0.13	0.52	0.76	3.44
7	2.57	2.53	2.51	0.19	0.00	0.75	3.46
8	2.50	2.47	2.51	0.12	0.53	0.74	3.44
9	2.57	2.53	2.51	0.15	−0.11	0.76	3.45
10	2.53	2.50	2.53	0.14	0.56	0.74	3.46
11	2.57	2.53	2.55	0.13	0.40	0.74	3.51
12	2.58	2.55	2.53	0.27	−0.11	0.77	5.54

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5. Hydrogen adsorption process

The accumulation of small molecules on a surface is known as adsorption, which can be classified as either physisorption or chemisorption, depending on the nature of the interaction between the adsorbate and the surface. Physisorption is governed by weak van der Waals forces, whereas chemisorption involves the formation of chemical bonds. The adsorption process is influenced by several key factors, including the host cluster, the type of adsorption, and the energy barrier between the adsorbate and the surface. A comprehensive understanding of hydrogen adsorption on Au_nY (n = 2–12) clusters can be obtained through detailed analysis of bonding characteristics, particularly examining the interaction of a hydrogen molecule or two dissociated hydrogen atoms within a specific chemical equilibrium. To gain fundamental insights into the adsorption processes of H₂ on Au_nY clusters, we calculate the adsorption energy and H–H bond length for both molecular and dissociative adsorption configurations using the following equations:

E_ads(Au_nY−H₂) = E(Au_nY) + E(H₂) − E(Au_nY−H₂) (4)

E_ads(Au_nY−2H) = E(Au_nY) + E(H₂) − E(Au_nY−2H) (5)

where E(Au_nY), E(H₂), E(Au_nY−H₂), and E(Au_nY−2H) with n = 2–12 represent the optimized energies of bare Au_nY, isolated H₂, molecularly absorbed Au_nY–H₂, and dissociatively absorbed Au_nY–2H, respectively. The results are summarized in Table 2. A preliminary analysis reveals that, compared to the bond length of isolated H₂ (0.75 Å),⁶³ the H–H bond length (d_H−H) in Au_nY–H₂ for n = 1–2, 4–6, 9, and 12 is significantly elongated, ranging from 0.76 to 0.85 Å. This increase in bond length indicates that H₂ undergoes activation upon adsorption on these Au_nY surfaces. In contrast, the distance between hydrogen atoms in Au_nY–2H clusters varies from 2.40 Å to 5.54 Å, confirming complete H₂ dissociation on the cluster surface.

The adsorption energies (E_ads) were calculated as the energy difference between the total energy of the reactants (Au_nY + H₂) and the products (Au_nY–H₂ or Au_nY–2H), as expressed in eqn (4) and (5). In essence, E_ads represents the minimum energy required to desorb hydrogen from the clusters surface, as listed in Table 2. Comparing the adsorption energy of molecular and dissociative adsorption configurations, we find that all computed E_ads values for the molecular adsorption (Au_nY–H₂) are positive, ranging from 0.05 to 0.29 eV, indicating that the formation of Au_nY–H₂ is thermodynamically favorable. For dissociative adsorption (Au_nY–2H), E_ads values range from −0.39 to 1.81 eV. Notably, the E_ads values for Au₂Y–2H, Au₃Y–2H, Au₇Y–2H, Au₉Y–2H, and Au₁₂Y–2H clusters are negative or zero (Au₇Y–2H), suggesting that dissociative adsorption on these clusters is endothermic and unlikely to occur spontaneously. This phenomenon can be attributed to the decrease in average binding energy for these clusters compared to their bare counterparts (Au₂Y, Au₃Y, Au₇Y, Au₉Y, and Au₁₂Y). In contrast, H₂ dissociation on Au_nY–2H (n = 1, 4–6, 8, 10 and 11) clusters is exothermic and thermodynamically favorable, as evidenced by the higher computed E_ads values for dissociative adsorption Au_nY–2H compared to molecular adsorption Au_nY–H₂. It is worth mentioning that molecular adsorption is more likely to occur for Au_nY with n = 2, 3, 7, 9, and 12. On the other hand, when H₂ approaches the surface of Au_nY (n = 1, 4–6, 8, 10, and 11), it first undergoes molecular adsorption. Subsequently, the hydrogen molecule may either desorb from the cluster surface or eventually undergo dissociation, forming strong atomic bonds with the cluster. The detachment of adsorbed H₂ molecules may dominate in certain cases, as it is influenced not only by adsorption energy but also by the activation barrier of the transition state and multiple intermediate states before reaching a stable dissociative configuration. A more detailed discussion on this topic will be provided in the following sections.

To better understand the binding nature of adsorbed hydrogen molecules on Au_nY (n = 1–12) clusters, we analyzed the densities of electronic states (DOS) for both molecular and dissociative adsorption configurations. The DOS results for several thermodynamically preferred configurations are illustrated in Fig. 3, while data for other species are provided in the ESI.† ⁴⁶ For each DOS graph in Fig. 3, both partial and total DOS are depicted. Solid lines represent spin-up (α) states, whereas dashed lines correspond to spin-down (β) states. As shown in Fig. 3, for species where physisorption is energetically feasible (Au_nY–H₂ with n = 3, 7), most of electronic states associated with adsorbed hydrogen (red line) appear on the low-energy side (below −13.0 eV), indicating a weak interaction between hydrogen and the cluster surface. These states are clearly separated from the electronic states of the cluster, which extend beyond −8.5 eV for n = 3 and −10.5 eV for n = 7, respectively. This indicates that the chemical bonding contribution between hydrogen and these clusters is relatively weak or potentially negligible. This observation aligns well with previous studies on molecular hydrogen adsorption in transition metal-doped Ag_n (n = 2–12), Au₁₀²⁺ or even [Mo₁₃S₁₃]²⁻ clusters, where van der Waals forces and/or electrostatic interactions between charge-polarized hydrogen molecules and cluster surfaces were identified as the dominant bonding mechanisms.^42,43,67

Fig. 3 Density of electronic states (DOS) for the most stable configuration of hydorgen adsorbed on Au_nY (n = 3–4, 6–8, and 11) clusters.

The DOS for dissociative configurations of Au_nY–2H (n = 4, 6, 8, 11) in Fig. 3, along with additional results for n = 1, 5, and 10 provided in the ESI,† ⁴⁶ exhibit a distinctly different behavior compared to their molecular adsorption counterparts. Remarkably, an analysis of the DOS spectra reveals an intriguing observation: the expected low-energy contribution of s-H₂ states, typically associated with molecular adsorption, disappears entirely in the dissociative configurations. Instead, the electronic states of hydrogen extend significantly toward higher energies, generally exceeding −10.5 eV, with the exception of n = 1 and 4, where they remain above −8.5 eV. This shift is attributed to the strong hybridization of valence s-electrons from hydrogen atoms with those of the cluster, leading to the formation of stable chemical bonds within these systems. Additionally, in most cases, the highest occupied molecular orbital (HOMO) states are predominantly contributed by s-Au orbitals, further reinforcing the role of gold in hydrogen dissociation mechanisms. It is important to note that bonding interactions are often accompanied by electron transfer processes. Therefore, these findings support the earlier conclusion that hydrogen adsorption preferentially occurs at Au surface sites.

To gain deeper insight into the dissociative hydrogen adsorption mechanism in Au_nY–2H (n = 1, 4–6, 8, 10 and 11) clusters, we computed possible reaction pathways linking the reactants to their final dissociated states for single H₂ adsorption and dissociation. Fig. 4 presents the hydrogen dissociation pathways for Au₄Y, Au₆Y, Au₈Y, and Au₁₁Y clusters, while additional data for AuY, Au₅Y, and Au₁₀Y are provided in the ESI.† ⁴⁶ The activation energy for hydrogen dissociation was determined by incorporating zero-point energy corrections and electronic energy values of the reactants and transition states (TS). Specifically, the activation barrier is quantified as the total energy difference between the reactants and the TS, offering insights into the feasibility of hydrogen dissociation on Au_nY clusters.

Fig. 4 Computed reaction pathways and relative energies (in eV) for H₂ dissociative adsorption on Au₄Y, Au₆Y, Au₈Y, and Au₁₁Y clusters. Intermediates and transition states are denoted as I_i and TS_i, respectively. Yellow, purple, and red spheres represent Au, Y, and H atoms, respectively.

As shown in Fig. 4, the interaction of H₂ with Au₄Y clusters follows a stepwise dissociative adsorption mechanism. Initially, molecular hydrogen preferentially binds to the transition metal atom Y with an adsorption energy of −0.16 eV. However, to activate the adsorbed H₂, the Au₄Y clusters must overcome two activation barriers (TS₁ and TS₂) associated with the dissociation process. The first activation barrier is 0.78 eV (+0.62 eV relative to the reactants at −0.16 eV), while the second barrier is 0.73 eV (+0.60 eV relative to the intermediate state I₁ at −0.13 eV). Before reaching the final dissociated product (Au₄Y–2H), the system passes through another intermediate state (I₂) at 0.44 eV. The final state, where the H₂ molecule is fully dissociated, has an energy of −0.27 eV, which is 0.11 eV lower than the reactant state (−0.16 eV), indicating a thermodynamically favorable process. A similar dissociative adsorption mechanism is observed for Au_nY clusters with n = 1, 5, 6, 8, 10 and 11). As detailed in the ESI,† the Au₅Y cluster follows a comparable pathway. The activation barrier for H₂ dissociation (TS₁) is 0.75 eV (+0.70 eV relative to the reactant state), followed by a significant energy decrease through the intermediate state I₁ (−0.04 eV). Ultimately, the system reaches a fully dissociated state, forming Au₅Y–2H with an energy of −0.52 eV, which is 0.47 eV lower than both the reactants and the H₂ adsorption state (−0.05 eV).

Similarly, for Au₆Y cluster, H₂ activation requires overcoming an energy barrier of 0.68 eV for the first transition state (TS₁, +0.55 eV relative to the reactant state). The system then proceeds through an intermediate state (I₁) with a slight energy drop of 0.21 eV before reaching the final dissociated state, which is 0.39 eV lower than the initial molecular adsorption state (−0.13 eV). A similar dissociative adsorption pattern is observed for AuY, Au₈Y and Au₁₀Y clusters. The activation barriers for the first transition state are 0.48 eV, 0.74 eV and 0.80 eV for the transition state TS₁ (0.36 eV, 0.62 eV and 0.66 eV relative to the reactant state), respectively. Before reaching their final stable states, Au₈Y and Au₁₀Y pass through intermediate states with energy drops of +0.56 eV and −0.28 eV, respectively. In contrast, the AuY cluster reaches its final state at −1.81 eV without any intermediate states. Interestingly, the Au₁₁Y cluster exhibits the lowest activation energy for H₂ dissociation among the studied clusters, with a barrier of 0.63 eV for TS₁ (+0.50 eV). The system transitions through an intermediate state (I₁, +0.46 eV) before fully dissociating into the most stable state, Au₁₁Y–2H, at −0.40 eV (0.27 eV lower than the reactants and the H₂ adsorption state, −0.13 eV). Comparing the activation barriers for H₂ dissociation across Au₅Y (0.75 eV), Au₆Y (0.68 eV), Au₈Y (0.74 eV), Au₁₀Y (0.80 eV), and Au₁₁Y (0.63 eV), it is evident that the Au₁₀Y cluster exhibits the highest energy barrier at 0.8 eV, suggesting a more challenging dissociative adsorption process compared to other clusters.

Although the final products of H₂ dissociation on the Au₄Y, Au₅Y, Au₈Y, and Au₁₀Y clusters exhibit relatively low energies of −0.27 eV, −0.52 eV, −0.53 eV, and −0.56 eV, respectively, the activation energy barriers for H₂ dissociation remain relatively high at 0.78 eV, 0.75 eV, 0.74 eV, and 0.80 eV. This suggests that while H₂ adsorption is energetically favorable for these clusters, dissociative adsorption is unlikely to occur without external stimuli, particularly for the Au₄Y and Au₁₀Y clusters. For the AuY cluster, the activation barrier for adsorption-dissociation is relatively low at 0.48 eV, and the final product has a significantly low energy of −1.81 eV. However, as previously mentioned, this cluster is known to be unstable, limiting its potential for real-world catalytic applications. In contrast, the Au₆Y and Au₁₁Y clusters exhibit the lowest activation energy barriers of 0.68 eV and 0.63 eV, respectively. This indicates that Au₆Y and Au₁₁Y could serve as promising superatoms for hydrogen storage applications.

6. Conclusion

In summary, we have systematically investigated the interaction of H₂ with small-sized Au_nY clusters (n = 1–12) using DFT calculations. Our findings highlight the crucial role of transition metal dopants in stabilizing cluster geometries and enhancing reactivity toward hydrogen adsorption and dissociation. We identified that the geometric structure, relative electronegativity of the dopant atom, and atomic coordination number (N) are key factors governing the preferred adsorption configurations. The Y atom exhibits a strong preference for high-coordination sites, favoring surface positions in smaller clusters (n = 1–5) before becoming gradually encapsulated by Au atoms in larger clusters (n = 6–12). Due to its relatively lower electronegativity (χ_Y = 1.22) compared to gold (χ_Au = 2.54), H₂ adsorption initially favors direct interaction with Y. However, as cluster size increases (n = 7–12) and the Y dopant attains higher coordination numbers, hydrogen adsorption shifts toward Au surface sites or Au–Au bridge positions. Notably, our results also indicate that molecular hydrogen adsorption does not significantly alter the structure of bare Au_nY clusters (except for Au₅Y). The adsorption of two dissociated hydrogen atoms preferentially occurs at Au–Au or Au–Y bridge sites, depending on cluster size and atomic arrangement. Average binding energy calculations reveal that the hydrogen adsorption on Au_nY (n = 4–12) generally maintains higher relative stability compared to their bare counterparts. Importantly, dissociative adsorption is unlikely to occur for Au_nY (n = 1, 4–5, 8, 10) clusters without external stimulation due to high energy barriers, while for n = 2, 3, 7, and 9 molecular adsorption is energetically preferred. Au₆Y and Au₁₁Y clusters exhibit remarkable stability and barrier-free dissociation pathways, making them promising candidates for hydrogen dissociation and storage applications. Our results provide a deeper insight into the interaction between H₂ and Au_nY clusters, including the adsorption site preference, the stability of adsorption configuration, the effect of impurities, possible reaction pathways, and energy barriers involved with this process. This work offers valuable guidance for future experiments and contributes to the development of alloys metal clusters as fundamental components in the design of innovative nanostructured materials for hydrogen catalysis and storage applications.

Data availability

The data supporting this article have been included as part of the ESI.†

Author contributions

Nguyen Van Dang: conceptualization, data curation, formal analysis, investigation, validation, writing – original draft, review and editing. Ngo Thi Lan: conceptualization, funding acquisition, data curation, validation, writing – original draft, review and editing. Nguyen Thi Mai: data curation, formal analysis, investigation, validation, review and editing. Son Tung Ngo: data curation, formal analysis, investigation, validation, review and editing. Phung Thi Thu: data curation, formal analysis, investigation, validation. Nguyen Thanh Tung: conceptualization, data curation, formal analysis, investigation, validation, writing – original draft, review and editing.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This research was financially supported by the National Foundation of Science and Technology Development (NAFOSTED) under the grant number 103.01-2021.109.

Notes and references

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5ra01901j

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